Dickson-stirling numbers

L. C. Hsu; Gary L. Mullen; Peter Jau Shyong Shiue

doi:10.1017/s0013091500023919

Dickson-stirling numbers

L. C. Hsu
, Gary L. Mullen
, Peter Jau Shyong Shiue

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The Dickson polynomial D_n (x, a) of degree n is defined by D_n (x, a) = ∑_i=0^[n/2] n/n-i (_i^n-i) (-a)ⁱ x^n-21, where ⌊⌋ denotes the greatest integer function. In particular, we define D₀ (x, a) = 2 for all real x and a. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of functions on finite sets in terms of their range values is also given.

Original language	English (US)
Pages (from-to)	409-423
Number of pages	15
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	40
Issue number	3
DOIs	https://doi.org/10.1017/s0013091500023919
State	Published - 1997

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/s0013091500023919

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title = "Dickson-stirling numbers",

abstract = "The Dickson polynomial Dn (x, a) of degree n is defined by Dn (x, a) = ∑i=0[n/2] n/n-i (in-i) (-a)i xn-21, where ⌊⌋ denotes the greatest integer function. In particular, we define D0 (x, a) = 2 for all real x and a. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of functions on finite sets in terms of their range values is also given.",

author = "Hsu, \{L. C.\} and Mullen, \{Gary L.\} and Shiue, \{Peter Jau Shyong\}",

year = "1997",

doi = "10.1017/s0013091500023919",

language = "English (US)",

volume = "40",

pages = "409--423",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "0013-0915",

publisher = "Cambridge University Press",

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TY - JOUR

T1 - Dickson-stirling numbers

AU - Hsu, L. C.

AU - Mullen, Gary L.

AU - Shiue, Peter Jau Shyong

PY - 1997

Y1 - 1997

N2 - The Dickson polynomial Dn (x, a) of degree n is defined by Dn (x, a) = ∑i=0[n/2] n/n-i (in-i) (-a)i xn-21, where ⌊⌋ denotes the greatest integer function. In particular, we define D0 (x, a) = 2 for all real x and a. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of functions on finite sets in terms of their range values is also given.

AB - The Dickson polynomial Dn (x, a) of degree n is defined by Dn (x, a) = ∑i=0[n/2] n/n-i (in-i) (-a)i xn-21, where ⌊⌋ denotes the greatest integer function. In particular, we define D0 (x, a) = 2 for all real x and a. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of functions on finite sets in terms of their range values is also given.

UR - https://www.scopus.com/pages/publications/21944439071

UR - https://www.scopus.com/pages/publications/21944439071#tab=citedBy

U2 - 10.1017/s0013091500023919

DO - 10.1017/s0013091500023919

M3 - Article

AN - SCOPUS:21944439071

SN - 0013-0915

VL - 40

SP - 409

EP - 423

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

IS - 3

ER -

Dickson-stirling numbers

Abstract

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